Question

A car travelling with $\dfrac{5}{7}$ of its actual speed covers 42km in 1hr 40min 48 sec. Find the actual speed of the car.
(a) $17\dfrac{6}{7}$ km/hr
(b) 25 km/hr
(c) 30 km/hr
(d) 35 km/hr

Answer 1

Hint: In order to solve this problem, we need to know the relation including the distance, speed and the time. The relation is as follows, $\text{Speed = }\dfrac{\text{distance}}{\text{time}}$ . All the units in the formula must match. Also, while converting the units we need to know that 60 seconds equals 1 minute and 60 minutes equal 1 hour.

Complete step-by-step answer:
We are given the car is travelling at $\dfrac{5}{7}$ the actual speed.
Let the actual speed of the car be x km/hr.
Then the current speed will be $\dfrac{5x}{7}$ km/hr.
The time taken by the car with this speed is 1hr 40 min 48 sec.
And the distance travelled by this car is 42 km.
We need to find the speed of the current car and then follow that actual speed.
The formula that has speed, distance and time is as follows,
$\text{Speed = }\dfrac{\text{distance}}{\text{time}}$ .
One which is important that we need to match all the units.
We are given the speed into km/hr, so we need to convert all the distances into km and all the time to hours.
Let’s first start by converting time into hours.
The time taken is 1hr 40 min 48 sec.
60 seconds on the clock equals one minute. But we have only 48 seconds.
Therefore, 48 seconds give $\dfrac{48}{60}$ minutes.
We need to add this value to 40 minutes.
The total minutes becomes $40+\dfrac{48}{60}=\dfrac{204}{5}$ minutes.
These are the total minutes in the total time taken now, we need to convert into hours.
But 60 minutes give 1 hour.
Hence, $\dfrac{204}{5}$ minutes give $\dfrac{204}{5\times 60}$ hours.
Solving this we get,
 Total hours of contribution by conversion of all the minutes is $\dfrac{17}{25}$ .
The total hours will become $1+\dfrac{17}{25}=\dfrac{42}{25}$ hours.
The total distance covered is 42 km.
Substituting the values, we get,
$\text{Speed}=\dfrac{42}{\dfrac{42}{25}}$
Solving this equation, we get,
$\text{Speed}=25$ km/hr.
Therefore, the current speed of the car is 25 km/hr.
 We also have shown that the current speed of the car is $\dfrac{5x}{7}$ km/hr, where x is the actual speed of the car.
Equating them both and solving for x we get,
$\begin{align}
  & 25=\dfrac{5x}{7} \\
 & x=\dfrac{25\times 7}{5} \\
 & x=7\times 5=35 \\
\end{align}$
Hence, the actual speed of the car is 35km/hr.
The correct option is (d).

Note: In this question, we need to find the actual speed and not the speed which is calculated directly by the formula. The main key thing here is to convert the units properly. In this, we did not need to change the units of the distance as it was already in km. We could have done the whole calculation in meters/sec and then convert back to km/hr and check for the answer. We will always get the same answer.